Exam 9: Conics, Systems of Nonlinear Equations and Inequalities, and Parametric Equations

Recall that the flight of a projectile can be modeled with the parametric equations: , where t is in seconds, v_o is the initial velocity, $\theta$ is the angle with the horizontal, and x and y are in feet. A projectile is launched at a speed of 200 ft/sec at an angle of 60° with the horizontal. Plot the path of the projectile on a graph.

Recall that the flight of a projectile can be modeled with the parametric equations: , where t is in seconds, ν_o is the initial velocity, θ is the angle with the horizontal, and x and y are in feet. A missile is fired from a ship at an angle of 56°, an initial height of 18 feet above the water's surface, and at a speed of 4430 feet per second. Will it be able to hit a target that is 2.4 miles away?

Graph the second-degree equation. (Hint: Transform the equation into an equation that contains no xy term.)

Find an equation for the parabola with vertex (0, 0) and focus (0, 3).

Write an equation for the parabola in standard form.

Solve each equation for y in terms of x. ,y< 0

Graph the second-degree equation. (Hint: Transform the equation into an equation that contains no xy term.)

Graph the second-degree equation. (Hint: Transform the equation into an equation that contains no xy term.)

Find the standard form of the ellipse with the following equation.

Graph the parabola and label the coordinates of the vertex.

Graph the curve defined by the parametric equations.

Find an equation for the parabola with focus (14, 9) and directrix x = 4.

Identify the conic section given by the following equation as a parabola, ellipse, circle, or hyperbola. 49x² - 4y² = 25

For the polar equation, graph the conic.

Two radio stations are located 180 miles apart along a coast. If a ship records a time difference of 0.0006 second and continues on the hyperbolic path corresponding to that difference, where will it reach shore? Round to the nearest mile. (Assume the speed of the radio signal is 186,000 miles per second.)

Graph the curve defined by the parametric equations. , ,t in [0, 2π]

The given rectangular equation defines a plane curve. Find the parametric equations that also corresponds to the plane curve.

Graph the hyperbola.

Find the equation of the hyperbola from the given graph.

Find the standard form of the equation of an ellipse with foci (-4, 0) and (4, 0) and vertices (-8, 0) and (8, 0).